How do you find the domain and range of g(x)=8/(8-3x)?
1 Answer
Feb 2, 2018
Explanation:
The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
"solve "8-3x=0rArrx=8/3larrcolor(red)"excluded value"
rArr"domain is "x inRR,x!=8/3
(-oo,8/3)uu(8/3,+oo)larrcolor(blue)"in interval notation"
"to find the range rearrange making x the subject"
y=8/(8-3x)
rArry(8-3x)=8
rArr8y-3xy=8
rArr-3xy=8-8y
rArrx=(8-8y)/(-3y)
"the denominator cannot equal zero"
rArry=0larrcolor(red)"excluded value"
rArr"range is "y inRR,y!=0
(-oo,0)uu(0,+oo)larrcolor(blue)"in interval notation"
graph{8/(8-3x) [-10, 10, -5, 5]}
